The Lilywhites rose into the top four of the Premier League table thanks to a dramatic comeback at the Tottenham Hotspur Stadium, where Brighton - without the suspended Roberto De Zerbi - took an early lead through a Pascal Gross penalty.
Tottenham spurned a handful of promising openings to draw level before the half-time whistle sounded, but the visitors were full value for their advantage in a stop-start battle, where fouls on both sides were commonplace.
However, Tottenham drew level just after the hour mark, as Pape Sarr's attempted cutback was intercepted by Lewis Dunk, but the Brighton defender could only deflect the ball onto the post, offering Sarr a simple tap-in from the rebound.
Sarr's strike preceded a raucous reception for the returning Son Heung-min - making his first appearance since the Asian Cup as a second-half substitute - although Brighton soon took the game by the scruff of the neck as Tottenham lost their defensive shape.
The Lilywhites weathered that defensive storm, though, and with six minutes of injury time on the board, a last-gasp Tottenham attack ended with Son squaring for fellow substitute Brennan Johnson to tap home at the back stick.
Mayhem reigned supreme inside the Tottenham Hotspur Stadium as Spurs recorded their fifth Premier League home win on the bounce, and Postecoglou unsurprisingly talked up his side's mentality and character after the contest.
"Fair to say the first half wasn't great. Part of that is because Brighton are a good side, they're well coached and very disciplined and we weren't. We just took a few liberties with our football, our effort and our work rate, there were a few things that we have been really good at this year but we just didn't do it in the first half," Postecoglou told reporters.
"I don't question the guys' character or mentality. We've done that a number of times this year but I was really disappointed the way we went about it in the first half. You can't get away from that. We've got to this point because of certain things we do and I was disappointed we went away from that, but you can't question the character.
"The response was very positive. It's easy in that kind of scenario to go into your shell and feel sorry for yourself but I've never felt that way with this group. They always respond in the right way when given that sort of guidance. I felt they took it on board in the second half and made a difference to the game."
Both Son and ex-Brighton man Yves Bissouma were only handed cameo appearances in the second half on the back of their respective Asian Cup and Africa Cup of Nations exploits, with Postecoglou keen not to overload the two international representatives.
"We were worried about fatigue, that's why we brought him on in the second half. He was ready to play, wanted to play," Postecoglou said on his decision not to bring Son back into the first XI.
"If we were desperate he probably would have started. But we had other options, that meant we could protect him. I think it was better for him that he came on and played the minutes he did."
As well as gleaning three precious points, Tottenham's triumph also saw the Lilywhites match the second-longest scoring streak in Premier League history, netting for the 36th top-flight fixture in a row.
Postecoglou's team have a full week to recuperate before Wolverhampton Wanderers visit North London for their next Premier League affair on February 17.